It is known that a right nilpotent congruence $eta$ on a finite algebra A is also left nilpotent [3]. The question on whether the left nilpotency class of $eta$ in less than or equal to the right nilpotency class of $eta$is still open. In this paper we find an upper limit for the left nilpotency class of $eta$. In addition, under the assumption that 1 $in$ typ{A}, we show that $(eta]^k=[eta)^k$ for all k$geq$1. Thus the left and right nilpotency classes of $eta$ are the same in this case.